A happy home is what the kids need. So stop drinking to hide your emotions first and foremost. You'll be generally more snappy and that isn't fair on them.
If you honestly feel that your relationship is beyond a point where happiness is found, then you should end it. Your current feelings will only grow and make you resentful to her if they are allowed to fester and you do not act upon it. This will in turn make a bad environment for the kids to live in.
You need to talk to her about this though. You need to tell her everything you've told us about your perception of this relationship, and your perception of her understanding of this relationship and why it doesn't make you happy. Then you need to talk to her to see how she feels about this relationship too. After this, you need to come to an agreement of how to proceed with the view to catering for your children's needs most, taking in to consideration all what you want, all what she wants and all that the kids need.
Should you both agree that ending it is ultimately for the best, then you need to be honest with your kids and reassuring.
Finally, if you do break up with her, show some respect to your relationship and just stay single until you, her and the kids are all settled in to a new routine. You don't want to appear like you've had another girl 'lined up', it'd be disgraceful.
Before all of this though, consider two things:
1) do I really want other women, or do I get excited because I know I cant / shouldn't be with them?
2) if my wife put a bit more effort in to her appearance, perhaps with some help from one of her more girly friends, would that help?